Here, we discuss the effect of external noisy magnetic fields on mesoscopic spin fluctuations that can be probed in semiconductors and atomic vapors by means of optical spin-noise spectroscopy. We also show that conventional arguments of the law of large numbers do not apply to spin correlations induced by external fields, namely, the magnitude of the 4th-order spin cumulant grows as ~N2 with the number N of observed spins, i.e., it is not suppressed in comparison to the 2nd-order cumulant. Moreover, this allows us to design a simple experiment to measure the 4th-order cumulant of spin fluctuations in an atomic system near thermodynamic equilibrium and develop a quantitative theory that explains all observations.